Recently, [1]} introduced the numerical technique known as
nested sampling [2]} to Bayesian phylogenetics.
This tries to simplify the multi-dimensional integral in
Equation REF 
into a one-dimensional integral over the cumulative distribution function
of the likelihood.
The latter can be numerically approximated using basic quadrature methods,
essentially summing up the area of polygons under the likelihood function.
The algorithm works by starting with a random sample of parameter values
from the joint prior distribution and their associated likelihood
scores.
Sequentially, the sample with the lowest likelihood is removed and replaced by
another random sample from the prior with the constraint that its likelihood
must be larger than the removed sample.
The approximate marginal likelihood is a running sum of the likelihood of these
removed samples with appropriate weights.
Re-sampling these removed samples according to their weights yields a posterior
sample at no extra computational cost.
Initial assessment of NS suggest it performs similarly to GSS.
As with SMC, NS seems like a promising complement to MCMC for both
approximating the posterior and marginal likelihood of phylogenetic models.
